Incorporating the neutrosophic framework into kernel regression for predictive mean estimation.

Area of Science:

• Statistics
• Survey Sampling
• Data Science

Background:

• Traditional statistics relies on precise data for population mean estimation, often leading to bias.
• Supplementary information in survey sampling can improve estimates but may introduce uncertainty.
• Handling indeterminate and vague information is crucial for robust statistical inference.

Purpose of the Study:

• To propose a novel neutrosophic predictive estimator for finite population mean.
• To minimize mean squared error (MSE) while providing accurate interval estimates.
• To address limitations of traditional methods in handling uncertain survey data.

Main Methods:

• Utilized the neutrosophic approach, an extension of classical statistics.
• Employed kernel regression for developing the neutrosophic predictive estimator.
• Performed simulation studies using Sine, Bump, and real-time temperature datasets with Gaussian kernel.

Main Results:

• The proposed estimator provides an interval range for the population mean, unlike single numerical values.
• This interval estimation enhances efficiency by minimizing mean squared error (MSE).
• The non-parametric neutrosophic estimator demonstrated superior performance compared to existing neutrosophic estimators across various bandwidth selectors.

Conclusions:

• The neutrosophic approach offers a powerful framework for statistical estimation with uncertain data.
• The proposed kernel regression-based neutrosophic estimator is more effective than traditional and adapted methods.
• This method improves the accuracy and reliability of population mean estimation in survey sampling.